Simplify the following expression: $\dfrac{90p^4}{81p}$ You can assume $p \neq 0$.
$ \dfrac{90p^4}{81p} = \dfrac{90}{81} \cdot \dfrac{p^4}{p} $ To simplify $\frac{90}{81}$ , find the greatest common factor (GCD) of $90$ and $81$ $90 = 2 \cdot 3 \cdot 3 \cdot 5$ $81 = 3 \cdot 3 \cdot 3 \cdot 3$ $ \mbox{GCD}(90, 81) = 3 \cdot 3 = 9 $ $ \dfrac{90}{81} \cdot \dfrac{p^4}{p} = \dfrac{9 \cdot 10}{9 \cdot 9} \cdot \dfrac{p^4}{p} $ $\phantom{ \dfrac{90}{81} \cdot \dfrac{4}{1}} = \dfrac{10}{9} \cdot \dfrac{p^4}{p} $ $ \dfrac{p^4}{p} = \dfrac{p \cdot p \cdot p \cdot p}{p} = p^3 $ $ \dfrac{10}{9} \cdot p^3 = \dfrac{10p^3}{9} $